Question

Find the value of \( x \) in the quadratic equation \( x^2 - 5x + 6 = 0 \).

• A. \( x = 2, 3 \)
• B. \( x = -2, -3 \)
• C. \( x = 1, 6 \)
• D. \( x = -1, 6 \)

Hint:

To solve a quadratic equation, factorize it and then solve for the values of \( x \).

Answer 1

The Correct Option is A

Step 1: Factorize the quadratic equation We are given the quadratic equation: \[ x^2 - 5x + 6 = 0 \] We need to factorize the equation. We are looking for two numbers whose product is \( 6 \) (the constant term) and whose sum is \( -5 \) (the coefficient of \( x \)). The numbers that satisfy this are \( -2 \) and \( -3 \). Step 2: Write the factorized form Thus, we can factorize the equation as: \[ (x - 2)(x - 3) = 0 \] Step 3: Solve for \( x \) To solve for \( x \), set each factor equal to zero: \[ x - 2 = 0 \quad \text{or} \quad x - 3 = 0 \] Solving these equations gives: \[ x = 2 \quad \text{or} \quad x = 3 \] Answer: Therefore, the values of \( x \) are \( 2 \) and \( 3 \). So, the correct answer is option (1).